The following references are cited in the specification. Disclosures of these references are incorporated herein by reference in their entirety.
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To achieve better quality control and reduce lead time, cluster tools are widely used for wafer processing in semiconductor manufacturing systems with a single-wafer processing technology that processes wafer one by one at a process module (PM). They provide a reconfigurable, flexible and efficient environment [Bader et al., 1990; and Burggraaf, 1995]. A cluster tool consists of several PMs, an aligner module, a wafer handling robot (transfer module), and loadlocks (LL) for wafer cassette loading/unloading, which are mechanically linked together in a radial way and computer-controlled. With a single-arm or dual-arm robot, such tool is correspondingly called a single-arm or dual-arm cluster tool. The latter is shown in FIG. 1.
A cluster tool with two LLs can be operated consecutively without being interrupted. Thus, it can operate in a steady state for most of time. Most prior studies [Chan et al., 2011; Ding et al., 2006; Perkinston et al., 1994; Perkinston et al., 1996; Venkatesh et al., 1997; Wu and Zhou, 2010; Yi et al., 2008; and Zuberek, 2001] were conducted to find an optimal periodical schedule. Only limited researches focused on transient states [Kim et al., 2013a; Kim et al., 2013b; Lee et al., 2012; Ahn and Morrison, 2010; and Wikborg and Lee, 2013] despite their increasing importance. With a given robot task sequence, the transient cycle time of a dual-arm cluster tool is minimized [Kim et al., 2013b]. Deadlock-free conditions are presented for lot switching periods of dual-arm cluster tools [Lee et al., 2012]. A model for transient and steady states is built [Ahn and Morrison, 2010]. When a robot task sequence is determined, an algorithm for an optimal transient cycle is proposed [Kim et al., 2013a, and Wikborg and Lee, 2013]. Since frequent switches between transient and steady states may lead to a deadlock problem, optimizing transient processes for cluster tools is recognized to be a big research challenge.
Some wafer fabrication processes, for instance, atomic layer deposition (ALD), require a wafer to visit more than once a PM under identical processing conditions. Due to such revisits, wafer processes are no longer a flow-shop, and the prior results without considering revisits, e.g. [Kim et al., 2013(a); and Wikborg and Lee, 2013], are no longer applicable. Such revisits make the optimal scheduling of transient processes much more challenging. Note that some well-developed theories or rules for a steady process [Lee and Lee, 2006] are not applicable for scheduling transient processes. Furthermore, deadlock often becomes an issue in a wafer fabrication process with revisit in a cluster tool [Lee and Lee, 2006]. It is certainly much more challenging to schedule a deadlock-prone system to obtain an optimal and deadlock-free schedule. In order to avoid deadlock and minimize makespan for a dual-arm cluster tool with wafer revisit, the studies [Wu and Zhou, 2010; and Zuberek, 2004] have developed Petri net models for performance evaluation and analyzed its cycle time under a swap strategy. They show that the steady state cycle time is determined by the time taken for completing one wafer at the step that has the heaviest workload. In fact, it is the lower bound of the cycle time for the system. However, this result is shown to be not correct in [Wu et al., 2013b], where a swap-based strategy is proposed and leads to a three-wafer cyclic schedule, which includes three local cycles for a revisiting process and three global cycles. It is also shown that the system can never enter its steady state under some conditions. In other words, the steady state-based analysis methods given in [Wu and Zhou, 2010; and Zuberek, 2004] are not applicable and the tool cannot reach the lower bound of cycle time. The multiple local and global cycles reduce the productivity of such cluster tools [Wu et al., 2013a]. Can a schedule with fewer local and global cycles improve the performance? The work [Wu et al., 2013b; and Qiao et al., 2013] answers this question by providing a schedule with two-wafer cycle, and also the one with one cycle only. It finds that the less the number of global cycles is, the shorter the robot waiting time is. Qiao et al. [2013] prove that one-wafer periodic schedule is optimal. They also provide a novel Petri net-based method to evolve a system from a transient state to a steady one. However, the transient process is not optimal despite its easy implementation according to the results to be presented in this work.
Although the minimum transient period is proposed for transient process scheduling [Kim et al., 2012], such conclusion is applicable to a non-revisiting case only. Their method cannot be extended a process with revisits without substantial research. The transient scheduling of dual-arm cluster tools with wafer revisiting to reach a desired steady state optimally is widely open as one has not found any study addressing it.
There is a need in the art for a method to obtain a schedule for dual-armed cluster tools with wafer revisiting process.